Nonlinear regression modeling via the lasso-type regularization

Generalized Lasso Regularization for Regression Models

Learning interactions via hierarchical group-lasso regularization.

We introduce a method for learning pairwise interactions in a linear regression or logistic regression model in a manner that satisfies strong hierarchy: whenever an interaction is estimated to be nonzero, both its associated main effects are also included in the model. We motivate our approach by modeling pairwise interactions for categorical variables with arbitrary numbers of levels, and the...

Integrating Ridge-type regularization in fuzzy nonlinear regression

In this paper, we deal with the ridge-type estimator for fuzzy nonlinear regression models using fuzzy numbers and Gaussian basis functions. Shrinkage regularization methods are used in linear and nonlinear regression models to yield consistent estimators. Here, we propose a weighted ridge penalty on a fuzzy nonlinear regression model, then select the number of basis functions and smoothing par...

Autoregressive process modeling via the Lasso procedure

The Lasso is a popular model selection and estimation procedure for linear models that enjoys nice theoretical properties. In this paper, we study the Lasso estimator for fitting autoregressive time series models. We adopt a double asymptotic framework where the maximal lag may increase with the sample size. We derive theoretical results establishing various types of consistency. In particular,...

Lasso Regularization Paths for NARMAX Models via Coordinate Descent

We propose a new algorithm for estimating NARMAX models with L1 regularization for models represented as a linear combination of basis functions. Due to the L1-norm penalty the Lasso estimation tends to produce some coefficients that are exactly zero and hence gives interpretable models. The novelty of the contribution is the inclusion of error regressors in the Lasso estimation (which yields a...